Volume of Rectangular Prism and Cylinder

Grade 6

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Warm Up

Find the Surface area of each rectangular Prism to the nearest tenth

5.5cm

2.3cm10cm

1. 2. 7.8 in.

6.2 in.5.4 in.

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Warm Up

Find the surface area of Cylinders:

4. r = 6mm, h = 10 mm

5. r = 3.5 ft, h = 24 ft

3. Write the formula for the surface area of a Cube in which each edge measures x units.

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Surface Area of a PrismThe surface area of a prism is the sum of the areas ofall the sides of the prism. The formula for the surfacearea of a prism therefore depends on the type of prism.

Surface Area of a CylinderThe surface area of a cylinder is the sum of the areasof the two bases and the lateral face of the cylinder.

surface area of a cylinder = 2*r2 + 2rh

Lets review what we have learned in the last lesson

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Types of prism

The name of a prism depends upon its base polygons.

If the bases are triangles, then it is a TRIANGULAR prism.

A RECTANGULAR prism has bases which are rectangles . The other types of prisms are pentagonal prism, hexagonal

prism and octagonal prism.

Surface Area of prism:

Surface Area of any prism = Lateral area + Area of two ends

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What is volume?

The amount of space occupied by an object is called its volume.

Cubic units are used to measure the volume. For example m3, cm3, in3, ft3 etc.

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Volume of Rectangular Prism

Prism is a 3D figure. The volume of a rectangular prism is given

by the formula: Volume = l × b × h Where l is the length of the rectangular prism. b is the width of the rectangular prism. h is the height of the rectangular prism.

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Practice

Example 1: Find the volume of the rectangular prism whose length is 12 cm, width 6 cm and height 8cm.

Solution: Volume = l × b × h Volume = 12 × 6 × 8 Volume = 576 cm3

The volume of the rectangular prism is 576 cm3.

Volume = l x b x h

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Practice

Example 2: Find the volume of the rectangular prism whose length is 6 in, width 6 in and height 4 in.

Solution: Volume = l × b × h Volume = 6 × 6 × 4 Volume = 144 in3

The volume of the rectangular prism is 144 in3.

Volume = l x b x h

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Volume of Cylinder

Cylinder is a 3D figure. The volume of a cylinder is given by the

formula: Volume = r2h Where r is the radius of the base of the

cylinder. h is the height of the rectangular prism. and pi = 3.14.

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Practice

Example 3: Find the volume of the cylinder whose radius is 10 cm and height 6cm.

Solution: Volume = r2h Volume = 3.14 × 102 × 6 Volume = 1884 cm3

The volume of the cylinder is 1884 cm3.

Volume = r2h

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Practice

Example 4: Find the volume of the cylinder whose diameter is 22 cm and height 14 cm.

Solution: Radius r = Diameter/2 = 22/2 = 11 cm Volume = r2h Volume = 3.14 × 112 × 14 Volume = 5319.6 cm3

The volume of the cylinder is 5319.6 cm3.

Volume = r2h

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Your Turn

Find the volume of the rectangular prism whose:

1. l=5 cm, b = 3 cm, h = 4 cm2. l=4 in, b = 3 in, h = 5 in 3. l=12 cm, b = 2 cm, h = 7cm 4. l=10 m, b = 5 m, h = 5 m 5. l=5 km, b = 5 km, h = 11km

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Your Turn

Find the volume of the cylinder whose:

6. r = 5 cm, h = 4 cm7. r = 10 in, h = 2 in 8. r = 1 km, h = 5 km9. r = 1 m, h = 1 m10. r = 2 cm, h = 2 cm

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Q1: Find the length of the rectangular prism whose area is 980 cm3, width is 10cm and height is 7 cm.

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Q2: Find the height of the cylinder whose area is 314 cm3, and radius is

10 cm.

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Q3: A match box measures 4cm by 2 cm by 2 cm. What will be the volume of the a packet containing a maximum of 12 such boxes?

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Let Us Review

The amount of space occupied by an object is called its volume.

The volume of a rectangular prism is given by the formula:

Volume = length × width × height

The volume of a cylinder is given by the formula:

Volume = π(radius)2x height

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You Had a Great Lesson Today!

Remember to practice what you have learned today